A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 31
Euclides Charles Mansford. PROPOSITION 10. PROBLEM . To bisect a given finite straight line , that is to divide it into two equal parts . 1 . Let AB be the given straight line . It is re- quired to divide it into two equal parts . 2 ...
Euclides Charles Mansford. PROPOSITION 10. PROBLEM . To bisect a given finite straight line , that is to divide it into two equal parts . 1 . Let AB be the given straight line . It is re- quired to divide it into two equal parts . 2 ...
Página 32
... straight line CF drawn from the given point CA shall be at right angles to the given straight line AB . B Because DC is equal to CE [ Con . ] , and FC is 3 . common to the ... a given point without it . It is required 32 EUCLID'S ELEMENTS .
... straight line CF drawn from the given point CA shall be at right angles to the given straight line AB . B Because DC is equal to CE [ Con . ] , and FC is 3 . common to the ... a given point without it . It is required 32 EUCLID'S ELEMENTS .
Página 33
... straight line CH drawn from the given point C shall be perpen- dicular to the given straight line AB . Join CF , CG . Because FH is equal to HG [ Const . ] , and HC is 3 . common to the two triangles FHC , GHC ; the two sides FH , HC ...
... straight line CH drawn from the given point C shall be perpen- dicular to the given straight line AB . Join CF , CG . Because FH is equal to HG [ Const . ] , and HC is 3 . common to the two triangles FHC , GHC ; the two sides FH , HC ...
Página 34
... given straight lines which cut one another . [ See Ex . to last two props . ] PROPOSITION 13. THOREM . The angles which one straight line makes with another straight line on one side of it , either are two right angles , or are together ...
... given straight lines which cut one another . [ See Ex . to last two props . ] PROPOSITION 13. THOREM . The angles which one straight line makes with another straight line on one side of it , either are two right angles , or are together ...
Página 43
... a point within the triangle ABC , prove that the sum of AO , BO , and CO is less than the sum of the three sides of the triangle . PROPOSITION 22. PROBLEM . To make a triangle of which the sides shall be equal to three given straight lines ...
... a point within the triangle ABC , prove that the sum of AO , BO , and CO is less than the sum of the three sides of the triangle . PROPOSITION 22. PROBLEM . To make a triangle of which the sides shall be equal to three given straight lines ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CEA axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join less Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal